# Questions tagged [bivariate-distributions]

For questions on bivariate distributions, the combined probability distribution of two randomly different variables.

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### Finding conditional expectation $E(Y|X>x)$ of Bivariate Normal distribution

$(X,Y)$ follows bivariate normal distribution with parameters $(\mu_1, \mu_2, \sigma_1^2, \sigma_2^2, \rho)$. Find the conditional expectation $E(Y|X>x)$. I know that $Y|x$ follows Normal ...
2answers
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### Find $\rho \left( {XY,Y} \right)$ given that $(X,Y)$ follows a bivariate normal distribution

Suppose $X$ and $Y$ have a bivariate normal distribution with parameters ${\mu _X} = {\mu _Y} = 0$, ${\sigma _X}^2 = {\sigma _Y}^2 = 1$, and $\rho = {\rho _{X,Y}} \ne 0$. I'm asked to find the ...
2answers
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### The $F(b,d)-F(b,c)-F(a,d)+F(a,c)\geqslant 0$ condition of joint CDFs

I'm trying to verify that a certain function of two variables $F(x,y)$ satisfies the conditions of a joint CDF. Showing that each condition holds has been fairly straightforward except, that is, for ...
1answer
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0answers
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### proving the effect of the covariance on the angle of the ellipse describing the distribution

I got the following home assignment: ...
0answers
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### bivariate conditional Gaussian

I want to calculate this probability in terms of $Q$-functions. $Pr\{X>m , Y>m , Y>X\}$ where $Y\sim N(0,\sigma_y^2)$ and $X\sim N(\mu,\sigma_x^2)$ and m is constant. Also $X$ and $Y$ are ...
0answers
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### Bivariate normal distribution, the 5th parameter

What does $\rho$ , the 5th parameter mean in the bivariate normal distribution ?
2answers
69 views

1answer
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### Let $f(x,y,z)=e^{-x-y-z},x>0,y>0,z>0$, and $=0$ otherwise, be the joint PDF of $(X,Y,Z)$. Compute $P(X=Y<Z)$. [closed]

Let $$f(x,y,z)=\begin{cases}e^{-x-y-z}, \ \ \text{x>0,y>0,z>0} \\0,\ \ \text{otherwise}\end{cases}$$ be the joint PDF of $(X,Y,Z)$. Compute $P(X=Y<Z)$. According to the textbook, the ...
1answer
100 views

2answers
110 views

1answer
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